Physics 1 – Air Wedge
AIR WEDGE
Aims
 To understand that an optical interference method can be used to measure small
distances.
 To measure the diameter of a wire by an optical interference method.
 To gain familiarity using a Vernier scale and determine the accuracy of your
measurements.
The Vernier Scale
A Vernier scale is a small moveable scale placed next to the main scale of a
measuring instrument. It allows us to make measurements to a precision of a small
fraction of the smallest division on the main scale of the instrument.
0
4
.6
.1
5
.8
.3
.7
.2
.9
.4
7
6
Vernier scale
1.0
.5
8
9
main scale
~ 4.3...
Figure 1
The following instructions describe how to correctly read the Vernier scale. Firstly,
read the measurement on the main (lower) scale which is aligned with zero on the
Vernier (upper) scale. You may find that using the magnifying lens and torch helps
you to read the scale more easily.
In the example of Figure 1 this gives a value of just over 4.35 and less than 4.4. The
accuracy of the measurement can be improved by reading the mark at which the lines
on the Vernier and the main scale line up. In figure 1 this point has been indicated in
bold for clarity and is at 0.18 or 0.68. Note the ambiguity between 0.18 and 0.68 as
the Vernier scale has two sets of markings on it. The correct number to take depends
on whether our first reading was above or below the 0.05 scale division on the main
scale. In figure 1 it was above 4.35 so we take the 0.68 reading.
The final measurement is given by summing the two readings of 4.3 and 0.68, giving
4.368mm. (Note: this Vernier scale measurement has units of millimetres; the Vernier
scales on spectrometers may be marked in degrees, minutes and seconds or degrees
and fractions of a degree.)
1
Physics 1 – Air Wedge
Part 1: Tutorial Question (15 mins)
In this experimental tutorial you are provided with two sets of clean glass plates
separated at one edge by a thin wire to produce a wedge shaped film of air. When the
wedge is viewed in monochromatic light, interference fringes which lie parallel to the
line of the wire are produced.
Travelling
microscope
Side view of
apparatus
Beam 1
Beam 2
Reflecting plate
Incident light
Glass plates
P
x
d
y
L
Figure 2
Figure 2 shows two beams of light entering the microscope:
Beam 1 is reflected at the upper surface of the bottom plate,
Beam 2 is reflected at the lower surface of the top plate,
P is the point of contact between the two glass plates,
x is the horizontal distance from P to the interference fringe being observed,
y is the vertical distance between the two plates at point x,
d is the diameter of the wire and
L is the distance from P to the centre of the wire.
Hence there is a path difference of 2y.
1.1
Find similar triangles within the diagram and hence express the path difference
in terms of d, x, and L.
Remember, there is a phase change of  radians (180 degrees), when light waves are
reflected off a medium having a higher refractive index.
1.2
Write down whether beams 1 and 2 have the same or different phase just
before entering the microscope. Hence, write down the equation for
destructive interference for this setup.
1.3
Explain why monochromatic light must be used as the source light for this
experiment.
2
Physics 1 – Air Wedge
Part 2: Observing Interference (20 mins)
If xn is the distance of the nth dark fringe from the point of contact of the glass plates
P, then:
2dxn
[1]
 n
L
where  is the wavelength of the sodium light used, 589 nm, and n is an integer.
In this part of the experimental tutorial you will setup the apparatus and take
measurements of the dark interference fringes then, knowing equation 1, compare
results with theoretical predictions.
 Use lens tissue to clean the two glass slides provided.
 Now make a wedge using the two slides and wire, as shown in Figure 1. Ensure
that the wire is completely parallel to the edge.
 Set up the apparatus as shown in Figure 1 using a sodium light as the source of
monochromatic light.
 Observe the fringes by eye, and then focus the microscope on them. The fringes
must be vertical lines and you should choose a region of the slide where the fringes
are clear and undistorted.
 Ensure that the box containing the glass plate setup is securely fastened to the
measuring table of the travelling microscope by using blue tac.
2.1
Measure the position xn of every tenth dark fringe over a range of fifty
fringes.
2.2
Measure L, the distance from the point P (the end of the glass slides) and the
position of the wire as accurately as possible.
Part 3: Analysis (15 mins)
3.1
Draw a graph of fringe position xn versus the number of fringe n. Your plot
should be a straight line.
3.2
Rearrange equation 1 to find what the gradient of the graph equals in terms of
L, and d.
3.3
Using your results for the gradient and given 589 nm for sodium light, find
the diameter of the wire d. Compare this with the accepted width of the wire, given by
the demonstrators, and discuss any differences.
3
Physics 1 – Air Wedge
Part 4: Using another slide (optional)
4.1
if:
Explain (and demonstrate) what happens to the separation of the dark fringes
(a) the wire is now replaced by a hair having diameter d 
1
the size of the wire.
2
(b) the light source is replaced by a mercury lamp.
Further work
The following questions are related to the topic covered by this experimental tutorial.


Example Book:
o Examples: L9
o Questions: L67, L68
Mastering Physics:
o Details of these will be sent by Paul Soler, P.Soler@Physics.gla.ac.uk
4
Physics 1 – Air Wedge
Demonstrators' Answers, Hints, Marking Scheme and Equipment List.
Marking Scheme
Section
1.1
1.2
1.3
2.1
2.2
3.1
3.2
3.3
Discretionary mark
TOTAL
Mark
1
1
1
1
1
1
1
1
2
10
Answers
1.1
y/x = d/L
therefore y = (2dx)/L
1.2
Different phase by  radians (180 degrees).
1.3
Condition for dark fringes in this case is that the path difference = integer
number of wavelengths.
So therefore: 2 y  m
1.4
To obtain interference the two sources (effectively) must have spatial and
temporal coherence which is obtained using a monochromatic source.
Note: Students may have difficulty producing straight interference fringes unless the
wire is completely perpendicular to the incoming light.
2.1/2.2 see table below
3.1
It is likely the students will be plotting their findings on graph paper and
y  y1
calculating the gradient by: M  2
x 2  x1
Expect different results from the following, but similar.
Dark
fringe
No.
0
10
20
30
40
50
Position
x (mm)
33.1
34.59
36.06
37.5
38.97
40.42
L (mm)
38.6
mm)
0.0005893
5
Gradient
M
0.1463
d (mm)
0.07774087
Physics 1 – Air Wedge
60
y = 0.1463x + 33.109
Position x (mm)
50
40
30
20
10
0
0
20
40
60
80
Fringe No.
3.2
3.3
the gradient M =
L
2d
L
2M
38.6  5.893  10 4
d 
 0.08mm
2  0.1463
d
Expect anything ~ 0.1mm
4.1
(a)/(b) the separation of the dark fringes would be reduced.
Equipment:
Sodium lamp
Travelling microscope
Slide box
Blue tac
2 x Slides
Piece of wire
Vernier calliper
Lens tissue
Magnifying torch
6
100